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Research Article | Open Access

Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative

Thanin Sitthiwirattham1, Rozi Gul2, Kamal Shah2,3( ), Ibrahim Mahariq4, Jarunee Soontharanon5, Khursheed J. Ansari6
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, Thailand
Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
College of Engineering and Technology, American University of the Middle East, Kuwait
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
Department of Mathematics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia
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Abstract

This article is devoted to investigate a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of Krasnoselskii's fixed-point theorem and Banach's contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results.

Keywords

Caputo-Fabrizio fractional derivativestability resultsfixed point resultsg-H-U stability
CLC number: 26A33, 34A08

References

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 4017-4037
DOI: 10.3934/math.2022222

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Cite this article:
Sitthiwirattham T, Gul R, Shah K, et al. Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative. AIMS Mathematics, 2022, 7(3): 4017-4037. https://doi.org/10.3934/math.2022222

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Received: 25 October 2021
Accepted: 02 December 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)